where a given source latent vector \(w_s\in \mathcal {W}^{L \times D}\)  (the
intermediate latent space in StyleGAN), audio-driven latent code \(w_a\in \mathcal {W}^{L \times D}\)  is optimized.
\(L\)  denotes the number of style layers at different levels, and \(D\)  denotes the dimension. \(\mathcal {L}_{\textnormal {reg}}\)  is regularization loss. \(\mathcal {L}_{\textnormal {ID}}\)  and \(G\)  are the identity loss and StyleGAN-based generator, respectively. By minimizing the hinge loss \(\mathcal {L}_\text{cos}\) , we find the sound-guided latent vector \(w_a\)  which generates an sound-guided image in the StyleGAN latent space. \(\lambda _\text{reg}\)  and \(\lambda _{ID}\)  are hyperparameters that control the strengths of the similarity loss term and the identity loss function \(\mathcal {L}_{\textnormal {ID}}\) . High values of \(\lambda _\text{reg}\)  and \(\lambda _{ID}\)  lead to maintenance of the content of the source image, whereas low values do not.
The source latent code \(w_s\)  means the randomly generated latent code from \(G\)  or the latent code obtained from the existing input image through GAN inversion [1]}, [2]}.
